Problems & Puzzles: Puzzles

1.- The Gordon Lee puzzle 

2.- Prime strings solution.gif (285 bytes) 

3.- Magic Squares with consecutive primes 

4.- Prime - magical squares solution.gif (285 bytes)  

5.- Find Pn =prime >61 such that Pn divides Pn+1*Pn+2 + 1 solution.gif (285 bytes) 

6.- Ray Ballinger suggestion 

7.- Palindrome - Primes: 2 questions solution.gif (285 bytes) 

8.- Primes by Listing solution.gif (285 bytes) 

9.- p1 + p2 + … pk = n m , m => 2 

10.- Primes associated to Primorials and Factorials 

11.- Distinct, Increasing & Decreasing Gaps 

12.- Period Length of 1/p solution.gif (285 bytes) 

13.- Magical Pentagrams solution.gif (285 bytes)

14.- Pal-Primes and sum of powers solution.gif (285 bytes)

15.- Narcissistic pal-primes  solution.gif (285 bytes)

16.- Consecutive primes and ending-digit 

17.- Weakly primes 

18.- Some Special Sums of Consecutive Primes 

19.- Primes on a Clock solution.gif (285 bytes)

20.- Reversible Primes 

21.- Happy Primes solution.gif (285 bytes)

22.- Primes and Persistence  solution.gif (285 bytes)

23.- Pal-primes adding consecutive primes solution.gif (285 bytes)

24.- Primes in several bases solution.gif (285 bytes)

25.- Composed primes  solution.gif (285 bytes)

26.- Honaker & Jud. McCranie puzzle  

27.- Heinz Rectangles  solution.gif (285 bytes)

28.- Heinz Stair-case  

29.- Pi = P i-1&nxtprm(P i-1), Pi = prime for i => 1  solution.gif (285 bytes)

30.- Queen attacking primes in a Knight’s tour solution

31.- The Average Prime number, APN(k) = S(Pk)/k solution.gif (285 bytes)

32.- Find couples of numbers like this (1033, 8) such that:
1033 = 8^1+8^0+8^3+8^3
 

33.- Find numbers like this:15551(palprime)= Fifteen Thousand Five Hundred Fifty One = 383 (palprime) 

34.- Prime Triplets in arithmetic progression  solution.gif (285 bytes)

35.- 1999 and the perfect numbers  solution.gif (285 bytes)

36.- Sequences of “descriptive primes”  solution.gif (285 bytes)

37.- Set of even numbers { ai } such that every ai + aj + 1 is prime   solution.gif (285 bytes)

38.- Sloane’s sequences solution.gif (285 bytes)

39.- The Mirrorable Numbers (By Mike Keith) 

40. The Pi Prime Search Puzzle (by Patrick De Geest) 

41. Palindromic Carnival (dedicated to Patrick De Geest)

42.- This week puzzle is to create a puzzle analog to other one.

43.-Palprime1*Palprime2 = Palindrome

44.-Enoch Haga Puzzle about Consecutive Primes

45.- Prime Solitaire (a puzzle based on a game proposed by Enoch Haga)

46.- Primes expressible as sum of consecutive primes in K ways

47.- p4 = a4 + b4 + c4 + d4, {a, b, c, d}>0

48.- P3 = a3 + b3 + c3, {P, a, b, c} = primes

49.- “If you are given K numbers of each from 0 to 9, find the maximum quantity of primes that can be formed using those 10K numbers”.  

50.- “The best approximation to Pi with primes”

51.- Pi such that Pi is Palprime & i = palindrome

52.- Sum of K consecutive primes equal to the sum of their reversible ones.

53.- Sequences of consecutive economical numbers. 

54.- Pair of primes of the form {p, 4p^2+1}

55.- Primes by Generation (Patrick De Geest)

56.- The Honaker's Constant

57.-  8757193191, another little puzzle from Mike Keith

58.- A particular sequence of k consecutive primes (by Enoch Haga)

59.- Six and the nine digits primes (by Jud McCranie)

60.- Generalized Cunningham chain (By Felice Russo)

61.- M(a, p)  = a^p - a + 1 ( by Jean Brette)

62.- The qs-sequence, (by T.W.A. Baumann)

63.- Another (3rd) Mike Keith's little puzzle.

64.- The Strange Ruler (TWA Baumann)

65.- Multigrade Relations

66.- The SOPF sequences

67.- The P/M-SOPF sequences

68.- The largest prime magic squares at the end of this Millennium (a puzzle suggested by Jaime Ayala)  

69.- Primeful Heterosquares  

70.- Primes Double Tree (a puzzle suggested by Paul Leyland)  

71.- Consecutive primes and Cunningham chains  

72.- Persistent Palprimes  

73.- A Collatz-like sequence.  

74.- SOD(26972593-1)  

75.- Prime numbers and the number 2000  

76.- z(n)=sigma(n) + phi(n) - 2n  

77.- Christmas Prime-Pine

78.- Primes by concatenating consecutive integers

79.- The Chebrakov's - by two months - Challenge  

80.- Twin primes - magic squares 

81.- Sophie Germain  primes - magic squares

82.- The Goldbach Comet

83.- The 6k+1 and 6k-1 boxes  

84.- Non-primes adding up to non-primes (by TWA)

85.- A puzzle about the Generalized Mills' theorem

86.- Disjoint sets A & B of consecutive numbers sharing the same set P of prime divisors

87.- Adding prime magic squares (a puzzle suggested by John E. Everett)

88.- A special set of odd primes

89.- The first palprime as a sum of consecutive composites

90.- The prime version of the taxicab problem

91.- Primes with the Smoothest Increasing Digits (SID primes)

92. A pile of prime-spheres

93.- Numbers such that the decimal and hexadecimal representation are the reverse of each other

94.  The Domino & the primes 

95. K consecutive primes p such that the decimal expansion of the reciprocal 1/p, for each p, has exactly a period of length (p-1)

96. The least K consecutive odd primes such that the sum of every two of them produces a distinct number

97. Consecutive numbers with the same "sum of prime factors" (SPF)

98. Curio 39  

99. Primes p such that R(p) is prime and p^2 = R(R(p)^2)  

100. Digital Prime k-tuplets

101. Digital Divisibility Tests  

102. Three squares a cube, all primes

103. N=a4+b4 = c4+d4

104. Numbers that are equal to the sum of cubes of its third parts (as strings)  

105. a^5 = b1^5+b2^5+...+bn^5

106. Prime-magic squares added up  to 2000

107. K Consecutive Smith numbers 

108. Methods for generating Smith numbers  

109. a1<a2<...<ak such that...

110. Dropping digits primes (by Patrick De Geest)

111. Spoof odd Perfect numbers  

112. Automorphic primes

113. Provable primes in Arithmetic progression

114. The Murad's generalization of the Collatz's sequences

115. Prime squares composed by no more than two digits

116. A=B+C, A*B*C is a primorial...

117. Certain p# +1 values

118. Primorial product numbers

119. Sophie-Germain & Twin, chains  

120. Primal Squares

121. THE  LEGEND  OF  YANG  HUI

122. Consecutive Twin primes

123. Two Frank Rubin's prime puzzles

124. Palindromic, Prime & Sophie-Germain pair of Magic Squares 

125. Primes through palindromes  

126. Some conspicuous probable primes

127.  Non adding prime sequences

128.  Sum of consecutive squared primes a square  

129.  Harshad Numbers

130.  The Hexagon of the 19 numbers

131.  Growing primes 

132.  Pascal Primes

133.  Pa - Qb = K  

134.  The 1379-Carrousel-Primes  

135.  Partitions into distinct primes with maximum product  

136.  Poor prime strings  

137.  Product of primes + 1, a square  

138.  Deletable primes  

139.  Sdf(x)=p  

140.  Primes Decades  

141.  Smarandache Prime Base representation of the natural numbers

142.  Optimal Assignation of Primes in several Patterns  

143.  The first and the last five primes  

144.  The Langford Prime Numbers

145.  The ISPP & SSPP functions 

146.  Solutions of A2 +X2 = Y2, A = odd 

147.  Twin & Reversible primes 

148.  Product of primes - 1, a square  

149.  Fermat 400 

150.  Primes type n+/- Fm, for m=0 to 4

151.  Euler-Rodríguez set of consecutive primes 

152.  The Prime Gears Cars Race  

153.  Espinosa's puzzle  

154.  Extension and Variation of the GC  

155.  Follow-up of the puzzle 151  

156.  One million doors  

157.  Zip primes  

158.  Sum of Cubes equal to Square of Sum

159.  A follow up to Puzzle 37

160.  s(n) and p(n) 

161. A Secret Code 

162. P2 + Q2 = p2 +q2  

163. P+SOD(P)

164. Sequences of Fermatian primes

165.  Bye Mr. Suzuki   

166. pn -1 =0 mod f(n)

167.  Primes m + 2 j & m - 2 j   

168.  Primes such that SOD2 = POD  

169. The unit and the sum of three signed prime-cubes 

170. Pseudoprimemania  

171. Perfect & Carmichael  numbers  

172. Minimal Length, prime-complete-rules  

173. Ruth-Aaron Triplets  

174. Primes & consecutive divisors  

175. Integer average & sets of consecutive primes  

176. Primes in a circle 

177. Primes in a square 

178. Shallit Minimal Primes Set

179. Prime Alphametics

180. Primes as a sum of squares

181. (N+k)/k primes 

182. Primes with zeros replaced

183. Perhaps a very simple question

184. Gronau's prime triplets

185. Differences between consecutive n^n values

186. Squareful Fibonacci numbers 

187. Triangles and Triangular numbers

188. Dividing large numbers

189. Squares and primes in a row

190. A follow up for the puzzle 188

191. P(n)=n(n+1)(n+2)(n+3) - 1

192. Reversible & Digit Complementary Prime Pairs

193. The Andersen's theorem & primes

194. The Palinpoints

195. Primes such that their squares are free of the digit D.

196. Consecutive integers with the same quantity of prime factors

197. Always composite numbers?

198. 2^a - 3^b = c

199. The Prime-Vampire numbers

200.  Ones from 1 to p (*)

201. The arithmetic function A(n)

202.  The n-th Omega recurrence

203.  Perfect primes

204. An old empirical observation

205.  Primes is in CI

206.  (N-k)/k primes

207.  The inventory sequences and the self-inventoried numbers

208.  Happy new Year 2003!

209. Triangles of primes

210. Jeff's numbers

211.  A beauty limit on prime numbers

212.  Substring reversion

213.  Hailstone Champion Sequences

214. Trotter's Curio

215. The Ulam Numbers

216 Primes in a square array

217. n in pn

218. Rupinski primes

219. Polignac numbers

220. p - k! primes

221. What are the next?

222. Equations with consecutive primes

223. Consecutive primes and powers of 2

224 Eccentric prime diagonals 

225. VIP (Very Sparse Primes)

226. Rolling Primes

227. Research Problem 1.75 

228. Sum of twin primes, a square

229. Primes and Hypercubes

230. Primes and a tower of cubes

231. k-Persistent primes

232. Primes and Cubic polynomials

233. A little twist

234. 2003, again

235. Dropping digits primes

236. A Broken Face

237. Alien neighbors

238. The hidden prime

239. psp (2) & n2 -2 numbers  

240.  Consecutive  numbers and consecutive prime factors

241.  Highly imperfect primes

242.  Sum of distinct squared primes

243.  Primes and squares in a square array

244.  Null Conjunction

245.  As 13

246.  The worms

247.  Consecutive Smith numbers

248.  Find one composite solution

249.  From Rudolf  to Rodolfo (magic squares and pandigital numbers)

250.  Euler, one more time.

251.  Pointer primes

252.  Kurchan squares

253.  Eureka

254.  Z=P2 - Q2

255.  k*p+1

256.  Jack Brennen old records

257.  Primes and sibling numbers  

258.  Primes and sibling numbers-II

259.  Not dividing any pandigital

260.  Chains of twins

261.  Symmetric prime constellations

262.  Semiprimes in arithmetic progression

263.  MagicAntiMagic Squares

264.  Antimagic Prime Squares

265.  Primes embedded

266.  Magic rectangles

267.  Talisman Squares

268.  23 primes in A.P.

269.  13 primes in A.P.

270.  Euclidean questions

271.  Prime gap tug of war

272.  P(n) & n

273.  Consecutive 'good' primes

274.  Sierpinski triangles from prime numbers

275.  Highly composite polynomials

276.  Prime factors of (x^n+y^n)/(x+y)

277.  Pi again

278.  The Rupinski's question

279.  Faride Firoozbakht asks for the next term

280.  3893257

281.  A follow up to Puzzle 24

282.  f(p) = f(p')

283.  Harshad Left Truncatable numbers

284 A+B=C | A.B.C = pk#

285.  μ(2^k-1) mod k

286.  Get a simple proof of this

287.  Multimagic prime squares

288.  Magic squares of (prime) squares

289.  Palprimes inside the infinite primes concatenated

290.  Primes on Platonic solid faces

291.  Primes embedding a given sequence

292.  Zigzag Primes

293.  Balanced primes

294. How to prove this?

295. Another Alphametic puzzle

296. An intriguing sequence

297. Queens on magic squares

298. Mersene, Mq = (8x)^2 - (3qy)^2

299. Collatz-like sequence of primes

300. UFO message?

301. One million of prime prime residues

302. Primes inside the sequence of primes

303. I'm such a square...

304. A larger square embedded

305. A new version of Puzzle 209

306. Generalized LYM Puzzle

307. Record Smith Numbers

308. AxB = N =A'xB'

309. A property of the prime '5'

310. DPT's on a knight's tour.  

311. Sum to a cube

312. Sequence of primes such that...

313. Squares having only k distinct digits

314. (f(n))=prime(n)

315. pn => pn-i + pi

316. Divide a square of primes.

317. Two dimensional constellation of primes

318. 31 = sigma(16) = sigma(25)

319. Approximations to π(n)

320. Dealing with primorials

321. Primes type n^4+4

322. Primeval primes as sum of primeval primes

323. Primes in a Sudoku solution

324. Self-descriptive numbers

325. Zeisel numbers

326. One more Firoozbakht curio sequence

327. Giuga numbers

328. Is this the largest?  

329. Odd abundant numbers not divided by 2 or 3.

330. σ(φ(σ(p)))=φ(σ(φ(p)))

331. The prime Russian mountain

332. Odd abundance

333. 'Magic squares' and primes

334. Faride & the 2004 year.

335. Prime values for σ(n).

336. sigma(n)<prime(n)

337. p inside p2.

338. Domino-Prime-Pyramid

339. Primes & persistence.

340. Resta's approach to Puzzle 337

341. Multiplicative persistence, Erdos style.

342. Primes on a dice.

343. One more Faride's question

344. Primes in Nature

345. Magic square of cubic primes

346. Happy 2006 

347.  Properties of numbers that have a Mersenne Number as a factor

348. 414347 prime string

349. 2d(n) = n + E

350. Primes & primorials

351. E796

352. φ(n!)

353. The first n2 primes in a matrix

354. Another prime game

355. Puzzle 232 in 4th order

356. A minimal set of K primes

357. Consecutive reversible primes

358. Ruth-Aaron pairs revisited

359. First N primes in a circle

360. Complementary divisors to make a prime

361. Multiply, or delete zeros

362. A sequence of primes.

363. A magnanimous company

364. P2 = Q*R  

365. P*Q = R*S

366. Three questions about the PGP

367. Two dice to produce prime numbers

368. Attained by invalid arithmetic

369. Approximations to unit adding prime reciprocals.

370. The first 13 numbers

371. A052215

372. Ask Dr. Matrix, prime version

373. Self primes

374. Self numbers

375. Powers which are the sum of initial primes

376. n=p*2^x

377. Add 2 to any digit  

378. Sequences embedded in decimal periods of fractions

379. SG primes and its prime average

380. A follow up to Puzzle 42

381. A sequence related to a special case of the Goldbach Conjecture

382. KL(29207), Prime or Composite?

383. Brougnard sequences

384. Prime Reverse Keith numbers

385 Follow up to Puzzle 104

386. CabTaxi, prime version

387. Prime curios in the Pascal's triangle rows?

388. Primes on a dice, again

389. Joe Crump and the search for solutions to 2nmod n=c 

390. 493009335

391. 9 dots, 8 lines

392. σ(x) = x+φ(x)

393. A follow up to Puzzle 128

394. No shared digits between composites and its prime factors

395. (2^n+3^n+4^n+5^n+6^n)/2 – 10

396. X*R=Y

397. 15984784979

398. 369293

399. Some more terms

400. 39883

401. Magnanimous primes

402. 1263560563

403. 833021343

404. Σ(x^x), for x=1 to n

405. R(38)

406. 1123

407. Prime Multidimensional Arithmetic Progressions

408. First primes embedded in the smallest number

409. Consecutive primes triplets

410. The largest magic square & primes...

411. Magic squares M & p(M)

412. Semimagic square of cubes

413. DPS in AP

414. Prime lucky number triplets

415. Sets of consecutive primes such that...

416. Prime numbers less than 2^18

417. M(e) reversed primes.

418. Honaker's ratio

419. Four SOPF questions

420. Another sequence of primes

421. Staircase of consecutive primes

422. 3N consecutive prime

423. K Consecutive even numbers such that...

424. Empty intervals between consecutive perfect powers

425. Consecutive numbers, increasing quantity of prime factors  

426. q = p +rad(p+1)  

427. Runs of consecutive numbers such that... (I)

428. Runs of consecutive numbers such that... (II)

429. Consecutive primes & biprimes

430. Grimm's conjecture

431. p = (q/r)3 + (s/t)3 

432. A nice pattern with 6 consecutive primes  

433. Three consecutive integers

434. σ(σ(x)) = σ(x)+x

435. φ(x) + σ(x) = k.x

436. 43 =4^2+3^3  

437. A special set of binary numbers

438. 1024383257

439. Fibonacci Primes Puzzle

440. σ(n)=2n-1

441. σ(n)+π(n)=k.n

442. Primes ending in 9

443. Sum of cubes of consecutive primes 

444. Pseudo twin primes

445. Consecutive integers with prime SPF

446. S(p, q)=p.q

447. Zeros on p.q

448. p+q not divided by 3  

449. Count N composites after p

450. K extended factors for sum of two consecutive primes 

451. Prime factors of n, φ(n) & σ(n)

452. (a^2)!+2^(a^2) = b*(1+a^2)

453. DPFP 

454. Number of primes of the form n^2 + 1

455. 1+σ0(n).σ(n) = n*rad(n)

456. Mersenne Primes as a sum of consecutive primes

457. Prime word embedded

458. Related to Puzzle 451

459. Related to Puzzle 457

460. Sqrt[p(x)*p(x+y)-1]= y

461. Consecutive squares + prime = prime.

462. p+q+r=3*q 

463. k.P(k)+(k+1).P(k+1)

464. p+4.x2  

465. Factorials

466. phi(n-1)=phi(n)=phi(n+1)

467. Primes in the last two digits

468. Primes & Semiprimes Gaps

469. 5040

470. p+2=semiprime

471. n and n^2 use only prime digits

472. What is the second solution?  

473. N = n^p + p^n

474. Two last puzzles for this 2008 

475. A question related to ABC Conjecture

476. A question related to Collatz Sequence

477. Sum of k primes = Product  of k integers

478. Factorials as sums of consecutive prime

479. P+1 & P+1+S are primes

480. Primes on an Dodecahedron

481. E.E-p=q

482. Two Bergot questions

483. p^2=a^2&b^2  

484. ABC conjecture and consecutive primes

485. Farideh's guess

486. Reserved for the Gods?

487. Follow up to Puzzle 485  

488. Follow up to Puzzle 487

489. Mersenne Primes & 0, 23 & 1535 

490. 2^n-2^k+1, a square

491. Sum of any combination is not prime

492. 59 and still counting...

493. p^p = x*a^2 + y*b^2

494. f(n)=product(prime(di))

495. P*R(P)+1 = Prime  

496. P*R(P)+1 = Palprime  

497. Sqrt[p^2+q^2- 9]

498. p*s+q*r is never a square

499. 6*7*8*9 - 1 is prime

500. 211896 

501. Three Consecutive primes a prime

502. Adding consecutive 2n+1 primes a prime

503. phi(x)*sigma(x) = x^2 - (1/n)*x

504. F(n) & G(n)

505. P(m^2 + 1) = n^2 + 1

506. Reversible primes again

507. phi puzzle from Farideh

508. phi(n)=phi(n+1)

509. S(n+1):=S(n)^2 - 2  

510. nrp(2^m) = m + 2

511. Primes reversing N, N^2, & N^3, ..., N^K

512. b^c=a(mod d)

513. Four consecutive primes

514. S(pi)= q mod r

515. Phi(Phi(x))

516. Fifty nine years old

517. φ(x) + σ(x+1) = 3x

518. Pi=prime(Pi-1)

519. Triangles with prime sides

520. Prime divides Repunits

521. p^p=p mod(q)

522. Three sets of k consecutive primes

523. Increasing residues

524. x = 1 (mod phi(x))

525. D= d1*P1 + d2*P2 +...dn*Pn

526. p2^2-p1^2 = n!

527. sigma(x) = 1 (mod x)

528. Prime quadratic residues

529. The prime-explosion Bergot graph

530. Twins pointing to equidistant trios

531. Two products of consecutive primes a power

532. Puzzle 529 re-loaded: sizing the prime nebulas.

533. phi(sigma(n^2)) = n(n+1)

534. The sum of any two terms a prime or...

535. The minimal seed Xo/Yo for square roots

536. Primes in several bases (again)

537. n^n = n mod [prime(n)]

538. (3n^2+3n+1) ^2 | (3n+1)^(3n+2) + 3n+2

539. n consecutive primes same residue modulo 4

540. b^(2^n)+c

541.- Emirps again

542.- Sigma (x)=q^n

543.- Primes as sum of powered consecutive primes

544.- Yet another  prime Prime Race

545.- 14 or 17<->25

546.- Non-Pandigital primes

547.- A064507

548.- dr(p*n) = dr(n)

549.- Better than 210

550.- Consecutive primes producing semiprimes

551.- Three nines & repunits

552.- p=k mod [prime(k)]

553.- SCN=PCP

554. P+10^n

555.- q=p(i) mod [p(i+1)]

556.- Follow up to Puzzle 554

557.- H(m, a)

558.- Goldbach decomposition & consecutive primes

559.- Mauldin / Tijdeman-Zagier Conjecture

560.- Same quantity of prime factors

561.- Square of consecutive prime & even numbers

562.- Heleen's sequence

563.- P=a^2+b^3

564.- Primorials & primes

565.- [(d)n] mod d^n = k

566.- Semiprimes in a given interval

567.- p1+...+pk = q1*...*qk

568.- SOPF(N)=SOPF(RN)

569.- Prime-Magic Hexagon

570.- Does this happen again?

571.- P(a)=P(b) mod(P(c)

572.- (P+Q)@3<>0

573.- Primes & its digital roots

574.- P.Q composed by only two distinct digits

575.- Primes | k leftmost digits are divided by p(k)

576.- Triangular Magic Triangles

577.- Happy prime Valentine day!

578.- The smallest prime concatenating the first k primes

579.- A triangular array with primes

580. An equivalence for twin primes

581. 142857

582. p.q=c^2+1

583. Traveling intertwined primes

584. Embedded but not overlapped prime factors

585. 37677869739

586. The best number is 73

587. Concatenating absolute differences

588. Squares sharing no one single digit

589. Palindromes multiplying consecutive primes

590. P-1 & P+1 with the same quantity of prime factors.

591. 1304119699

592. p.(p-1)=q&(q+1)

593. Primes by transportation

594. 999997600699

595. p*q -> p^2 + p*q + q^2

596. 12*n*(n+2)+1

597. A follow up to Puzzle 596

598. A18781

599. Weird numbers

600. Follow up to Puzzle 599

601. Pair of primes (p, q) such that...

602. T(73)=37*73

603. p=(q*r+s)/2

604. Primes in 2&3&4&...&n

605. Follow up to Puzzle 604

606. Puzzle 738 from Claudio Meller's site

607. A zeroless Prime power

608. 2^(2^n)+k

609. Rectangling the square.

610. Rectangling the square-II.

611. Puzzle 2-3-5-7.

612. Prime-Doublets.

613. Curio sum of primes.

614. Always composite by insertion

615. Abs[R(n/3)-n]<=1

616. Primes by dupplicating some digit

617. Concatenating & superposing

618. GCD(1+P, S)

619. Odd midpoints

620. 2012

621. Puzzle 411 revisited

622. Primes as concatenation of two squares

623. p^2+3pq+q^2=r^2

624. Nice integer quotients

625. Sum of squares of prime divisors

626. Frank Rubin, kissing primes

627. Nested Carmichael numbers

628. Fermat Pseudoprimes

629. Non-primitive Carmichael numbers

630. Gap between p(n-1) & p(n+1)

631. Follow up to Puzzle 630

632. [R(n)+1]@n=0

633. Palindromes & Pandigitals

634. Primes in Collatz trajectory

635. 34155

636. Primorial as product of palindromes

637. Factorials as product of palindromes

638. Special integer quotients

639. Sigma (n+12m) = Sigma(n)+12m

640. A sequence of semiprimes.

641. Cunningham Chains of semiprimes.

642. N=A&B=A+B^3

643. 134757431

644. 123 Curio

645. Generalized Dudeney Numbers

646. Curio 364

647. Shifted alphabet rows

648. P^2 = A^2&B^2

649. An algorithm for this conjecture

650 Triangular, Primes & Powers of 2

651 6866683

652 Recursively Pi+1 = POD(Pi) + 1

653 R(p) is n^n.

654 Factors for p(n)#+/-1

655 pq+rs, perfect square.

656 Primes using certain quantity of digits

657 Look and say sequence

658 Find primes such that...

659 Sandwiched palindromes

660 Exotic primes

661 Carpet palindrome Persian art style

662 547716131821

663 Pandiagonal prime magic squares

664 The queen covering the chessboard

665 (p+q)*(q+r)=m^n

666 Columns = Rows

667 Puzzle 77

668 Fortyfive

669 2013 and 2014

670 The same sum of divisors

671 Most Perfect Magic Squares

672 sigma(sigma(x)) + sigma(x) = 3x

673 Sudoku & primes, again

674 Concatenating the squares of consecutive primes

675 p = -1+2^57885161

676 primes in a row such that...

677 primes in a row such that... II

678 Find the least vector of integers such that...

679 Prime-proof odd integers

680 The largest palindrome prime-proof odd integer race

681 Stanley Antimagic Squares

682 Stanley Antimagic Squares-II

683 Rubin's puzzle

684 Primes in N dice

685 Follow up to puzzle 683

686 Filling the grid (Le Monde puzzle)

687 17769643

688 Follow up to Puzzle 687

689 Pandiagonal and twin primes

690 Unreachable primes

691 Conjectures related to Gilbreath's scheme

692 Consecutive prime gaps biprimes

693 Prime Chemical Compounds

694 S(p,q)=p&q

695 Pandiagonal & twin primes

696 1801

697 Puzzle 105, revisited

698 Others as 129

699 Special prime pandigital magic squares

700 p & q primes such that ...

701 Alphametic magic square

702 Adding emirps to a cube

703 Dividing a set of primes in other two

704 Find a prime such that...

705 2213

706 Palindromes generating palindromes

707 The smallest sum for a set...

708 Find sets of k consecutive primes such that...

709 Primes P=A&B such that...

710 6252893229398 & non-semiprimes

711 Composites with the exactly the same digits than its prime factors

712 Primes or squares

713 Primes between perfect powers

714 Composites that remain composites when...

715 phi(x + n) = sigma(x - n)

716 Problem 9 of...

717 Associative squares Stanley

718 A follow up to Puzzle 700

719 Extension to Ruth Aaron pairs

720 x^2&y^2 or y^2&x^2 squares

721 p(i)= DR(p(i-1))&(p(i-1)\10)

722 2^m-1 consecutive integers having m prime factors

723. Pandiagonal magic squares of consecutive primes

724. Extending the OEIS sequence A229908

725. The ABA numbers

726. Completing the OEIS sequence A235031

727. Extending the OEIS sequence A235680

728. Consecutive Moran numbers (extending the OEIS sequence A235397)

729. Consecutive Hoax numbers (extending the OEIS sequence A235766)

730. Trio of Consecutive Achilles numbers

731. Stanley Antimagic squares  of consecutive primes

732. Sum of cubes a square

733. Integers equal to the sum of the squares of their prime divisors.

734. "Common Sigma, Uncommon Clique" Numbers

735. Consecutive primes such that the sum of their digits generates another set of consecutive primes.

736. Associative Stanley squares of consecutive primes

737. Maximize  log(s) / log(maxPrimeFactor(s))

738. Special Cunningham Chains

739. Carmichael numbers of special form

740. Misprinted product, find the correct one

741. Find the smallest set of distinct primes such that...

742. Prime-Golygons

743. The least largest prime in a 4x4 magic square

744. The smallest prime such that...

745. A number 20 digits large, best qualified

746. A follow up to Puzzle 742 (about golygons)

747. A second follow up to Puzzle 742 (about golygons)

748. A third follow up to Puzzle 747 (about 3D-golygons)

749. Prime magic cubes

750. A special 5x5 prime magic square

751. Named primes producing primes

752. Palindromes as sum of the first k primes

753. Prime lattices

754. Quantity of primes in P+Q

755. Upside Down Magic Squares

756. Primonacci

757. Follow-up to Puzzle 756

758. Associative magic cubes of prime numbers

759. Palindrome primes in A.P.

760. A087711

761. On certain consecutive primes p & q

762. Conjecture from Ribenboim's book

763. P(n) = P(n)^P(n+1) mod (P(n)+P(n+1))

764. N integers in a row such that...

765. pa = qb + rc.sd

766. A Follow up to Puzzle 764.

767. A second Follow up to Puzzle 764.

768. Primes as m sums of triangular numbers.

769. Magic squares and consecutive twin primes.

770. Eygptian Fraction Magic Square

771. First P primes in a square.

772. Entry 1363 by Claudio Meller

773. Necklaces with k primes 

774. S(i) and Rad(i)

775. Triangles and consecutive primes

776. Ten consecutive integers such that...

777. Ultra magic squares

778. A follow-up to Puzzle 774

779. A first follow-up to Puzzle 776

780. A second follow-up to Puzzle 776

781. A second follow-up to Puzzle 776

782. Prime-Generating non-polynomials

783. A sequence of composite integers

784. Find some more solutions

785. Extend this table

786. Looking for certain set of integers.

787. Fibonacci as sum of two consecutive primes.

788. P&p(i)^2&RP

789. Almost primes Fibonacci numbers.

790. Prime Langford pairing

791. Inserting consecutive primes

792. Prime numbers equal quantity of digits...

793. Entry 1399 from Claudio Meller's site

794. Prime Generalized Palindromes

795. Primes reversing substrings

796. Looking for certain palprimes

797. Primes and perfect numbers related

798. A nice puzzle by Kamenetski.

799. Follow-up to Puzzle 798.

800. A nice numbers sequence.

801. A nice stepladder of primes

802. A follow up to Puzzle 801

803. Panprimmatics

804. Palindromes and primes

805. Prime gaps containing...

806. Extended n-Parasitic numbers

807. Symmetrical compositions of twin primes

808. Palprimes that remain...

809. Two linked Goldbach prime-stairs

810. Sum of consecutive triangulars and primes

811. Primes and Sum of consecutive triangulars-II

812. Other chains of primes

813. Symmetrical compositions of consecutive twin primes

814. Primes and squares such that...

815. Another prime pine

816.Primes between n*k and n*(k+1)

817. 2016  and prime numbers

818. A follow up to Puzzle 814

819. A follow up to Puzzle 314

820. The  Sunduram's sieve

821. Prime numbers and complementary sequences

822. About OEIS sequence A193890

823. String of digits 1379 full of primes

824. Insecure numbers

825. Primes type Liouville

826. Primes and Pascal Triangle

827. A sieve for twin primes

828. A sequence of primes such that... are free of the digits 2,0,1,

829. Dividing the first k prime to obtain new primes.

830. Entry 1439 from Claudio Meller's site.

831. Rings of primes.

832. Follow-up to Puzzle 828.

833. A special set of integers.

834. A274071.

835. Goldbach squares.

836.  Bills serial numbers.

837. Kaprekar prime numbers

838. Follow up to Puzzle 833.

839. Follow up to Puzzle 835.

840. Second follow up to Puzzle 835.

841. Symmetrical compositions of consecutive pairs of cousin primes

842. Multiple or divisor

843. Looking for more Kaprekar prime numbers

844. Primes inside Sudoku solutions

845. 31 consecutive integers with an even quantity of prime factors

846. A follow up to Puzzle 844

847. Consecutive primes with the same Collatz length.

848. p(0)nq is prime for n=0,1,2,...k

849. 9x9 Magical square and pandigitals.

850. The wagon prime.

851. Puzzle 827 revisited

852. Primes and convolution

853. The Euler polynomial again

854. Follow up to Puzzle 853

855. Second follow up to Puzzle 853

856. Cascade of primes 4k+1

857. A second cascade of primes 4k+1.

858. Updating the Puzzle 203.

859. A follow-up to Puzzle 203.

860. Primes of the Mersene primes reversed.

861. Puzzle 1467, by Claudio Meller

862. Redo Puzzle 861

863. 2017 a new prime year

864. 10958, the only hole...

865. Area Magic Squares

867. Follow up to Puzzle 833

868. Magic squares 3x3 and palprimes

869. Prime nested magic squares

870. Prime nested magic squares-II

871. Claudio Meller 1476

872. Integers (p^2)*Q

873. Follow-up to Puzzle 871

874.Consecutive integers with increasing or non decreasing quantity of divisors

875.Vector of primes that generates distinct primes

876.Prime Tuples

 


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